Tennis Balls & Planets

A fool wants to tie a rope around the earth. So he buys a rope of 40,000 KM and ties it around the world. His neighbour, also a fool, wants to do the same only he wants the rope on sticks 1 meter above the ground.

How much more rope does he need?
And how much more rope do you need when you use a tennis ball instead of the earth?

Answer

6 meters 28 centimeters.

x=2*PI*(r+1)-2*PI*r
x=2*PI*r+2*PI-2*PI*r
x=2*PI
x=6.28

It does not matter what the radius of the circle is. You always need 2*pi meters more of rope for each additional meter of radius added.Hide

Comments

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It absolutely DOES matter what the radius of the earth is! The only time that "2*pi" applies is when you are increasing the applied radius by 1 unit. Still, keep them coming, you are my favorite riddle writer at Braingle!

No, the radius of the original ball does not matter. Adding 6.28 meters of rope will always increase the diameter of the circle by 2 meters, which will make the rope 1 meter off the earth (or tennis ball) all the way around.

Think of it another way: suppose there was no tennis ball, and there was just a tiny knot of rope. To make a circle 2 meters wide you need 6.28 meters of rope. The reason it doesn't seem right is that we are used to perceiving the AREA of a circle instead of its CIRCUMFERENCE.

The answer is quite correct. It asks for how much MORE rope is needed and the same extra amount is required no matter what. If you want an explanation that uses calculus then given C = 2*Pi*R then dC = 2*Pi*dR which tells us that the change in circumference is 6.28 times the change in radius and there is no reference to the size of the original radius. It's an oldie but a goodie!